Lesson Plans: 6.NS.B.4 Greatest Common Factor

(This lesson should be adapted, including instructional time, to meet the needs of your students.)

Background Information
Content/Grade Level / The Number System/Grade 6
Unit/Cluster / Compute fluently with multi-digit numbers and find common factors and multiples
Essential Questions/Enduring Understandings Addressed in the Lesson / Why might you need to find the greatest common factor of 2 whole numbers?
Numbers have factors and multiples, common factors and common multiples and a relationship among them.
Standards Addressed in This Lesson / 6.NS.B.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor.
It is critical that the Standards for Mathematical Practice be incorporated in ALL lesson activities throughout each unit as appropriate. It is not the expectation that all eight Mathematical Practices will be evident in every lesson. The Standards for Mathematical Practicemake an excellent framework on which to plan instruction. Look for the infusion of the Mathematical Practices throughout this unit.
Lesson Topic / Greatest Common Factor(This lesson only does GCF.)
Relevance/Connections / 6.NS.A.1 Common Factors Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions.
Student Outcomes / Students will be able to find the greatest common factor of two given whole numbers.
Prior Knowledge Needed to Support This Learning / 4.OA.4 Find factor pairs and determine whether a whole number is prime or composite.
Method for determining student readiness for the lesson / Use the Warm-up/drill as a formative assessment to determine the level of understanding for finding factors of a number.
Learning Experience
Component / Details / Which Standards for Mathematical Practice does this address? How is each Practice used to help students develop proficiency?
Warm Up / Factor Review:
  • Divide the students into 2 groups. One group will list all the factors of a number (24); the other group will list all the factors of a different number (54).
(Teacher checks for understanding while writing each factor on a sticky note and placing on the board to use in Activity 1.) / .
Motivation / To help review the purpose of a Venn Diagram, set up a Venn diagram concerning pets – one circle labeled “I have a dog”, one labeled “I have a cat”. Students will write their name on a given sticky note. During warm-up, students will place their name in the appropriate circle or outside the circle.
Discuss the results to review the use of a Venn Diagram.
Activity 1
UDL Components
  • Multiple Means of Representation
  • Multiple Means for Action and Expression
  • Multiple Means for Engagement
Key Questions
Formative Assessment
Summary / UDL Components:
  • Principle I: Representation is present in the activity. Students use prior knowledge as they factor a number. Use of Venn Diagrams activates students’ knowledge through visual imagery.
  • Principle II: Expression is present in the activity. Students physically interact with instructional materials by examining their Venn Diagrams through a gallery walk.
  • Principle III: Engagement is present in the activity. The gallery walk prompted students on when and how to ask peers and their teacher for assistance. This task allows for active participation, personal response, evaluation and reflection.
Directions:
  • Set up a Venn Diagram with one circle titled “Factors of 24”, the other titled “Factors of 54”.
  • Using the factors on the sticky notes (Warm-up), have students select a sticky note and place the factor on the Venn Diagram.
  • Facilitate the discussion so that the students check for accuracy of the diagram.
  • Have students identify the common factors and then identify the Greatest Common Factor (GCF).
  • Assign a number (1- 100) to each student. Have students write all of the factors of their number on small squares of paper, one factor per square.
  • Give each student a piece of yarn to make a circle on a hard surface (notebook, textbook, etc.), placing their small squares of paper in the circle.
  • Direct students to find a partner and combine yarn circles to make a Venn Diagram, placing their factors appropriately.
  • Results can be shared using the document camera or have students walk around the room to see others Venn Diagrams.
  • Discussion questions:
  • What do see?
  • What did you notice when both numbers were even? Both were odd? One even and one odd?
  • What did you notice when both numbers were large? Both were small? One large and one small number?
  • Can the GCF be a prime number? Why or why not? A composite number? Why or why not?
/ Students will make sense of problems and persevere in solving them by planning a solution pathway to find the factors of numbers instead of jumping to a solution.
(SMP#1)
Students attend to precision as they communicate precisely with others as they find the factors of numbers.
(SMP#6)
Look for and make use of structure by requiring students to apply general rules for finding the factors of numbers.
(SMP# 7)
Look for and express regularity in repeated reasoning as they factor their number and continually evaluate the reasonableness of their intermediate results.
(SMP# 8)
Activity 2
UDL Components
  • Multiple Means of Representation
  • Multiple Means for Action and Expression
  • Multiple Means for Engagement
Key Questions
Formative Assessment
Summary / UDL Components:
  • Principle I: Representation is present in the activity. Prior knowledge is activated an authentic student-centered scenario that models key concepts regarding greatest common factor. Different color note cards are assigned to represent baseball and football as the students perform the activity of finding the greatest common factor.
  • Principle II: Expression is present in the activity. It provides an option for physical activity as they work with their assigned partner to determine the greatest common factor.
  • Principle III: Engagement is present in the activity. The activity allows for participation, exploration and experimentation and also invites students to individually and personally respond, evaluate, and reflect.
Directions:
Part A
  • Provide the following problem:
Jacob is packaging 18 baseball cards and 12 football cards to sell at a yard sale. Each packet will have the same number of cards, using cards of only one sport in a package. What is the greatest number of cards he can place in each packet? How many packets will there be for each sport? Use 2 different colored note cardsto represent baseball and football cards.
  • Assign partners to determine how the problem can be solved using the cards provided.
  • Have one pair of students share their solution/strategy.
  • Lead a discussion to have students realize that the successful numbers are factors:
  • What different combinations would work for each set of cards? (1 package of 18, 2 packages of 9, and 3 packages of 6 for 18. 1 package of 12, 2 packages of 6 and 3 packages of 4 for 12)
  • Which combinations work for both sets of cards? (common factors)
  • Which combinations will give the greatest number of cards in a package? (3 packs of6, 2packs of 6)
  • What is the greatest common factor?
  • Show students how to list the factors for 18 and 12, circle the common factors and identify the greatest common factor.
18: 1, 2, 3, 6, 9, 18
12: 1, 2, 3, 4, 6, 12
Part B
  • Provide each group of students a problem on a card to solve by finding the GCF. Leaving the card at each station, have students rotate around the room to complete additional problems. (see below)
  1. Hot dogs come in packages of 8. Rolls come in bags of 6. Darla wants to buy the same number of hot dogs and rolls. What is the smallest number of hotdogs Darla can buy?
(Answer is 24 hot dogs.)
  1. Ms. Skinner was working with the volunteer club to make bags of treats for the nursing home visit. She bought a bag of 18 chocolates and a bag of 12 pens. If each bag contains the same amount of treats, how many pens will be in each bag? (Answer is 2 pens.)
  1. Mrs. Wheatley was working on a project with her students. She bought two spools of ribbon in lengths of 6 inches and 24 inches. She needs to cut the ribbon into pieces of equal length. What is the greatest possible length of the pieces? (Answer is 6 inches.)
  1. A convenience store has bags of apples and bags of oranges. The store has a total of 64 apples and 40 oranges. Each bag contains the same number of pieces of fruit. What is the greatest number of pieces of fruit each bag could contain? (Answer is 8 pieces of fruit.)
  1. Mr. Brian is planning a staff party. Plates come in packs of 8 and napkins come in packs of 16. Mr. Brian wants to buy the same number of napkins and plates. What is the smallest number of plates Mr. Brian can buy? (Answer is 16 plates.)
  1. Raj and Amy bought cookies. Raj bought 12 cookies and Amy bought 8 cookies. The cookies are sold in packages only of a certain size. How many cookies are in each package? (Answer is 4 cookies are in each package.)
  1. Mrs. White’s students are making school spirit packs. They have 24 bumper stickers and 18 window clings. Every pack must have the same contents, and there should be no leftover items. What is the greatest number of packs they can make? How many of each item will be in each pack? (Answer is 6 packs and each pack contains 4 bumper stickers and 3 window clings.)
  1. Sandi bought two pieces of wood in lengths of 24 inches and 20 inches. She needs to cut the wood into pieces of equal length. What is the greatest possible length of each piece? (Answer is 4 inches.)
  1. A box of chocolate chip cookies holds 24 cookies. A box of peanut butter cookies holds 12 cookies. A group of friends share the cookies in each box. Each friend got an equal number of chocolate chip and peanut butter cookies from each box. What is the greatest number of friends in each group? How many peanut butter cookies did each friend get? (Answer is 6 friends and 2 peanut butter cookies.)
  1. Juan bought 12 cupcakes and Mika bought 15 cupcakes. The cupcakes are sold only in packages of a certain size. How many cupcakes are in each package? (Answer is 3 cupcakes.)
  • Have students return to their seats to discuss the activity with the whole class.
/ Students should make sense of problems and persevere in solving them as they plan a solution pathway instead of jumping to a quick solution. (SMP# 1)
Model with mathematics by expecting students to apply the mathematics concepts they know about GCF and LCM and then reflect on whether their results makes sense and how they could improve or revise their model.
(SMP# 4)
Students are attending to precision as they express numerical answers with a degree of precision that is appropriate for the context of the problem.
(SMP#6)
Look for and make use of structure as they apply mathematical rules for GCF and LCM to these specific problems.
(SMP# 7)
Closure / Exit ticket problem:
There are 18 math students and 24 science students touring the Science Center in Baltimore. They will be assigned a tour group. Each group must have the same number of either math or science students. What is the greatest number of students in each group?
Supporting Information
Interventions/Enrichments
  • Students with Disabilities/Struggling Learners
  • ELL
  • Gifted and Talented
/ Students with Disabilities/Struggling Learners:
  • Use of multiplication chart to find all factors of a number
  • Use of graph paper to shade in arrays to determine factors of a number
  • Centimeter cubes or 2 color counters could be used to help solve the group problems.
ELL
  • Identify the words that students will have difficulty with and help them become acquainted with them.
  • Allow them to use cubes or color counters.
Gifted and Talented
  • How do you think GCF be used in real life?

Materials / Yarn
Small Squares of Paper
Sticky Notes
Poster/chart paper
Colored Note Cards
Graph Paper
Centimeter Cubes
Two Color Counters
Technology / document camera
calculator
Resources / Van de Walle, John A., Teaching Student-Centered Mathematics, Grades 5-8

Page 1 of 2